Aquifers are inherently heterogeneous at various observation scales. Characterizing the heterogeneity at a scale of our interest generally requires information of hydrological properties at every point in the aquifer. Such a detailed hydraulic property distribution in aquifers requires numerous measurements, considerable time, and great expense, and is generally considered impractical and infeasible. The alternative is to utilize a small number of samples to estimate the variability of parameters in a statistical framework. That is, the spatial variation of a hydraulic property is characterized by its probability distribution estimated from samples. The distribution of porosity data in an aquifer is normally distributed. The spatial distribution of storage coefficient might be lognormally distributed. Hydraulic conductivity distributions are usually reported to be lognormally distributed. Based on such a statistical approach, one can treat hydraulic properties or their logarithms (e.g., n, log K) as a Gaussian random field and analyze the uncertainty in groundwater flow and transport modelling using Monte Carlo Simulation.
A. Watch the videos below and answer the questions that follow.
Probabilistic modeling:
Equally plausible realizations, ensemble mean and variance:
Questions:
- What is a Monte Carlo simulation?
- What is an Monte Carlo flow and plume realization?
- What is an ensemble?
- What does ensemble average plume distribution mean?
- What does ensemble variance mean?
- Why is it that the concentration variance exhibits a bimodal distribution?
- Where does the maximum variance occur? Why?
- How can a variance map be used to guide monitoring network design for additional data collection?
- How can Monte Carlo simulation be used to show all of the possible "events" that could or will happen?
- How can Monte Carlo simulation be used to compute the probability of each possible outcome?
- How can Monte Carlo simulation be used to account for risk in decision making and quantitative analysis in the presence of uncertainty?
- Why is that the probabilistic structure in head, seepage velocity, solute concentration dramatically different: lnK as input is Gaussian, head as output is approximately gaussian, seepage velocity and solute concentration as output are strongly skewed distributed?
- Can a variance map always be used to characterize uncertainty?
B. Develop a MAGNET model that can reproduce the above animations, generating multiple likely realizations of conductivity, flow, and solute plume distributions, computing real-time probability distributions, and write a 1 page memo on heterogeneity, uncertainty, and risk-based decision making and on the probabilistic structure of groundwater flow and transport variables.